Many languages have an interesting class of nouns, the pluralia tantum, which have restricted number possibilities when, in some sense, they should not. Thus English binoculars has no singular, which is worth noting (that is, it is not predictable). True, there are other nouns denoting items consisting of two significant parts which behave similarly (spectacles, trousers.. .); indeed they are subject to 'middle-size generalizations' (Koenig 1999). But there are two reasons to note such nouns. First there are many English nouns equally denoting items consisting of two significant parts which are unremarkable in this respect: bicycle, bigraph, Bactrian camel, couple, duo.. . And second, there are languages with number systems roughly comparable to that of English in which the equivalents of binoculars and trousers are normal count nouns: Russian binokl', French pantalon. While pluralia tantum are of continuing interest, it is typically only the English type which is considered. But these familiar examples offer an entry point to a collection of lexical items, some with much stranger behaviour, lurking between the semi-predictable and the unexpectedly defective. In particular, some instances demonstrate that we cannot maintain the general assumption that the 'internal' morphosemantic specification of a paradigm cell and its 'external' morphosyntactic requirement are necessarily identical. I therefore set out a full typology of these fascinating nouns, so that their significance can be more fully appreciated. I start from the notion of canonical noun, and calibrate the different non-canonical properties according to a set of orthogonal criteria.